518 research outputs found

    Periodic Solution for a Complex-valued Network Model with Discrete Delay

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    For a tridiagonal two-layer real six-neuron model, the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature. In the present paper, we extend this two-layer real six-neuron network model into a complex-valued delayed network model. Based on the mathematical analysis method, some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts. Our sufficient conditions obtained by the mathematical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method. Computer simulation is provided to illustrate the correctness of the theoretical results

    On delayed genetic regulatory networks with polytopic uncertainties: Robust stability analysis

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    Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results

    Bio-inspired Dynamic Control Systems with Time Delays

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    The world around us exhibits a rich and ever changing environment of startling, bewildering and fascinating complexity. Almost everything is never as simple as it seems, but through the chaos we may catch fleeting glimpses of the mechanisms within. Throughout the history of human endeavour we have mimicked nature to harness it for our own ends. Our attempts to develop truly autonomous and intelligent machines have however struggled with the limitations of our human ability. This has encouraged some to shirk this responsibility and instead model biological processes and systems to do it for us. This Thesis explores the introduction of continuous time delays into biologically inspired dynamic control systems. We seek to exploit rich temporal dynamics found in physical and biological systems for modelling complex or adaptive behaviour through the artificial evolution of networks to control robots. Throughout, arguments have been presented for the modelling of delays not only to better represent key facets of physical and biological systems, but to increase the computational potential of such systems for the synthesis of control. The thorough investigation of the dynamics of small delayed networks with a wide range of time delays has been undertaken, with a detailed mathematical description of the fixed points of the system and possible oscillatory modes developed to fully describe the behaviour of a single node. Exploration of the behaviour for even small delayed networks illustrates the range of complex behaviour possible and guides the development of interesting solutions. To further exploit the potential of the rich dynamics in such systems, a novel approach to the 3D simulation of locomotory robots has been developed focussing on minimising the computational cost. To verify this simulation tool a simple quadruped robot was developed and the motion of the robot when undergoing a manually designed gait evaluated. The results displayed a high degree of agreement between the simulation and laser tracker data, verifying the accuracy of the model developed. A new model of a dynamic system which includes continuous time delays has been introduced, and its utility demonstrated in the evolution of networks for the solution of simple learning behaviours. A range of methods has been developed for determining the time delays, including the novel concept of representing the time delays as related to the distance between nodes in a spatial representation of the network. The application of these tools to a range of examples has been explored, from Gene Regulatory Networks (GRNs) to robot control and neural networks. The performance of these systems has been compared and contrasted with the efficacy of evolutionary runs for the same task over the whole range of network and delay types. It has been shown that delayed dynamic neural systems are at least as capable as traditional Continuous Time Recurrent Neural Networks (CTRNNs) and show significant performance improvements in the control of robot gaits. Experiments in adaptive behaviour, where there is not such a direct link between the enhanced system dynamics and performance, showed no such discernible improvement. Whilst we hypothesise that the ability of such delayed networks to generate switched pattern generating nodes may be useful in Evolutionary Robotics (ER) this was not borne out here. The spatial representation of delays was shown to be more efficient for larger networks, however these techniques restricted the search to lower complexity solutions or led to a significant falloff as the network structure becomes more complex. This would suggest that for anything other than a simple genotype, the direct method for encoding delays is likely most appropriate. With proven benefits for robot locomotion and the open potential for adaptive behaviour delayed dynamic systems for evolved control remain an interesting and promising field in complex systems research

    NeuroPod: a real-time neuromorphic spiking CPG applied to robotics

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    Initially, robots were developed with the aim of making our life easier, carrying out repetitive or dangerous tasks for humans. Although they were able to perform these tasks, the latest generation of robots are being designed to take a step further, by performing more complex tasks that have been carried out by smart animals or humans up to date. To this end, inspiration needs to be taken from biological examples. For instance, insects are able to optimally solve complex environment navigation problems, and many researchers have started to mimic how these insects behave. Recent interest in neuromorphic engineering has motivated us to present a real-time, neuromorphic, spike-based Central Pattern Generator of application in neurorobotics, using an arthropod-like robot. A Spiking Neural Network was designed and implemented on SpiNNaker. The network models a complex, online-change capable Central Pattern Generator which generates three gaits for a hexapod robot locomotion. Recon gurable hardware was used to manage both the motors of the robot and the real-time communication interface with the Spiking Neural Networks. Real-time measurements con rm the simulation results, and locomotion tests show that NeuroPod can perform the gaits without any balance loss or added delay.Ministerio de Economía y Competitividad TEC2016-77785-

    Complex oscillations in the delayed Fitzhugh-Nagumo equation

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    Motivated by the dynamics of neuronal responses, we analyze the dynamics of the Fitzhugh-Nagumo slow-fast system with delayed self-coupling. This system provides a canonical example of a canard explosion for sufficiently small delays. Beyond this regime, delays significantly enrich the dynamics, leading to mixed-mode oscillations, bursting and chaos. These behaviors emerge from a delay-induced subcritical Bogdanov-Takens instability arising at the fold points of the S-shaped critical manifold. Underlying the transition from canard-induced to delay-induced dynamics is an abrupt switch in the nature of the Hopf bifurcation

    Monostability and multistability of genetic regulatory networks with different types of regulation functions

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    The official published version of the article can be found at the link below.Monostability and multistability are proven to be two important topics in synthesis biology and system biology. In this paper, both monostability and multistability are analyzed in a unified framework by applying control theory and mathematical tools. The genetic regulatory networks (GRNs) with multiple time-varying delays and different types of regulation functions are considered. By putting forward a general sector-like regulation function and utilizing up-to-date techniques, a novel Lyapunov–Krasovskii functional is introduced for achieving delay dependence to ensure less conservatism. A new condition is then proposed for the general stability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the upper and lower bounds of the delays. Our general stability conditions are applicable to several frequently used regulation functions. It is shown that the existing results for monostability of GRNs are special cases of our main results. Five examples are employed to illustrate the applicability and usefulness of the developed theoretical results.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the U.K. under Grant BB/C506264/1, the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 60504008 and 60804028, the Program for New Century Excellent Talents in Universities of China, and the Alexander von Humboldt Foundation of Germany

    Human Conscious Experience is Four-Dimensional and has a Neural Correlate Modeled by Einstein's Special Theory of Relativity

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    In humans, knowing the world occurs through spatial-temporal experiences and interpretations. Conscious experience is the direct observation of conscious events. It makes up the content of consciousness. Conscious experience is organized in four dimensions. It is an orientation in space and time, an understanding of the position of the observer in space and time. A neural correlate for four-dimensional conscious experience has been found in the human brain which is modeled by Einstein’s Special Theory of Relativity. Spacetime intervals are fundamentally involved in the organization of coherent conscious experiences. They account for why conscious experience appears to us the way it does. They also account for assessment of causality and past-future relationships, the integration of higher cognitive functions, and the implementation of goal-directed behaviors. Spacetime intervals in effect compose and direct our conscious life. The relativistic concept closes the explanatory gap and solves the hard problem of consciousness (how something subjective like conscious experience can arise in something physical like the brain). There is a place in physics for consciousness. We describe all physical phenomena through conscious experience, whether they be described at the quantum level or classical level. Since spacetime intervals direct the formation of all conscious experiences and all physical phenomena are described through conscious experience, the equation formulating spacetime intervals contains the information from which all observable phenomena may be deduced. It might therefore be considered expression of a theory of everything
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